Once you receive the credit card, neither activating the card nor choosing to leave it inactivated can change your credit score. However, once you activate the card and start using it, but miss repaying the card debt in time, your credit score could be negatively impacted. As missing repayment deadlines can also mean having to pay interest on the debt, you may consider budgeting your spending to ensure you can pay off the debt in full each month.
In general, credit card companies check your credit score when reviewing your credit card application, but only with your permission. Note that a single credit inquiry doesn't impact your credit score much but multiple credit checks in a short time could make you appear credit hungry when a future lender or credit provider pulls out your credit report. This might raise a red flag and make it difficult for you to qualify for new credit.
Whether or not your application gets approved doesn’t directly impact your credit score. However, when you are rejected for a credit card, it is recorded on your credit report. When you apply for another credit card immediately after rejection, it might lead to your application getting declined again. It’s advisable to work out why your application was declined and improve that area before applying again to increase your chances of getting approved for a credit card.